{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<center><font face=\"黑体\" size=4>《机器学习基础实践》课程实验指导书</font></center>\n",
    "<br>\n",
    "<br>\n",
    "<center><font face=\"黑体\",size=4>第9章  半监督学习</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{实验目标}$\n",
    "\n",
    "掌握和理解半监督学习的基本理论知识，常见的半监督学习算法的原理与实现方法。\n",
    "\n",
    "$\\textbf{实验内容}$\n",
    "\n",
    "$\\textbf{9.1 半监督学习简介}$\n",
    "\n",
    "在很多实际的机器学习任务中，由于数据的标记信息很难得到，我们只拥有少部分具有标记信息的数据，而大部分数据是未标记的。由于传统的监督学习方法只能在有标记的数据样本上进行学习，未标记的样本不能直接用于监督学习，造成数据使用上的浪费。此外，由于未标记的样本和有标记的样本都是从同样的数据源独立同分布采样而来，未标记样本所包含的数据分布的信息对于机器学习算法的学习过程也是大有裨益。因此，如何在学习过程中充分利用有标记和无标记的样本，来提升学习的性能成为机器学习领域的一个研究热点。半监督学习就是一种让学习方法不依赖于外界交互、自动地利用未标记样本来提升学习性能的机器学习框架。\n",
    "\n",
    "$\\textbf{9.2 图半监督学习}$\n",
    "\n",
    "给定一个数据集，可以将其映射为一个带权图，图中的顶点对应于数据集中的样本，图的边表示数据样本之间的相似度，相似度越高，对应的边上的权值越大。图半监督学习的过程就是利用有标记的样本以及样本之间的相似性对未标记的样本的标记信息进行预测，从而利用已标记数据和未标记数据来提升学习的性能。\n",
    "\n",
    "假设训练数据集$D=D_l \\cup D_u$，其中$D_l=\\{(\\textbf{x}_1,y_1),(\\textbf{x}_2,y_2), \\ldots ,(\\textbf{x}_l,y_l)\\}$是有标记训练样本的集合，\n",
    "$D_u=\\{\\textbf{x}_{l+1},\\textbf{x}_{l+2}, \\ldots ,\\textbf{x}_{l+u}\\}$是未标记的训练样本的集合，令$m=l+u$，表示训练样本的总数。基于训练集$D$，可以构建一个带权图$G=(V,E)$，其中$V= \\{\\textbf{x}_1, \\ldots , \\textbf{x}_l, \\textbf{x}_{l+1}, \\ldots ,\\textbf{x}_{l+u}\\}$是训练样本组成的顶点的集合，边集$E$可以通过一个亲和矩阵$\\textbf{W}$表示，矩阵$\\textbf{W}$表示，矩阵$\\textbf{W}$的第$i$行第$j$列元素$w_{ij}$表示样本$\\textbf{x}_i$和$\\textbf{x}_j$之间的相似度。相识度的计算如下所示。\n",
    "\n",
    "\\begin{equation}\n",
    "w_{ij} = \\begin{cases}\n",
    "e^{-(\\frac{\\Vert \\textbf{x}_{i}-\\textbf{x}_{j}\\Vert_{2}^{2}}{2\\sigma^{2}})} & if \\ i \\ne j\\\\\n",
    "0 & otherwise\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "假设从训练数据中学习得到的模型为$f: \\textbf{X}→Y$。对于相似的训练样本其类别标记也应该相似，因此可以定义关于模型f的能量函数\n",
    "\n",
    "\\begin{equation}\n",
    "E(f) = \\frac{1}{2}\\sum_{i=1}^{m}\\sum_{j=1}^{m}w_{ij}(f(\\textbf{x}_{i})-f(\\textbf{x}_j))^2\\\\\n",
    "E(f) = \\frac{1}{2}(\\sum_{i=1}^{m}d_i f^2(\\textbf{x}_{i})+\\sum_{j=1}^{m}d_{j}f^2(\\textbf{x}_{j})-2\\sum_{i=1}^{m}\\sum_{j=1}^{m}f(\\textbf{x}_i)f(\\textbf{x}_j))\\\\\n",
    "E(f)=\\sum_{i=1}^{m}d_i f^2(\\textbf{x}_j)-\\sum_{i=1}^{m}\\sum_{j=1}^{m}f(\\textbf{x}_i)f(\\textbf{x}_j)\\\\\n",
    "E(f) = \\textbf{f}^{T}(\\textbf{D}-\\textbf{W})\\textbf{f}\n",
    "\\end{equation}\n",
    "\n",
    "其中，$f=(f(\\textbf{x}_1),f(\\textbf{x}_2),…,f(\\textbf{x}_l), f(\\textbf{x}_{l+1}),…,f(\\textbf{x}_m))$表示模型在训练集上的预测结果组成的向量，$\\textbf{D}$是一个对角矩阵，对角线上的数据元素$d_i$为亲和矩阵$\\textbf{W}$的第$i$行数据元素的和。\n",
    "\n",
    "采用分块矩阵表示，可以将矩阵$\\textbf{W}$、矩阵$\\textbf{D}$和向量$\\textbf{f}$分别表示为\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{W}=\\begin{bmatrix}\n",
    "\\textbf{W}_{ll} & \\textbf{W}_{lu}\\\\\n",
    "\\textbf{W}_{ul} & \\textbf{W}_{uu}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{D}=\\begin{bmatrix}\n",
    "\\textbf{D}_{ll} & \\textbf{0}_{lu}\\\\\n",
    "\\textbf{0}_{ul} & \\textbf{D}_{uu}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{f}=\\begin{bmatrix}\n",
    "\\textbf{f}_{l} & \\textbf{W}_{u}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "则能量函数$E(f)$可以进一步表示为\n",
    "\n",
    "\\begin{equation}\n",
    "E(f) = \\textbf{f}^{T}(\\textbf{D}-\\textbf{W})\\textbf{f}\\\\\n",
    "E(f) = \\begin{bmatrix}\n",
    "\\textbf{f}_{l}^{T} & \\textbf{W}_{u}^{T}\n",
    "\\end{bmatrix}(\\begin{bmatrix}\n",
    "\\textbf{D}_{ll} & \\textbf{0}_{lu}\\\\\n",
    "\\textbf{0}_{ul} & \\textbf{D}_{uu}\n",
    "\\end{bmatrix}-\\begin{bmatrix}\n",
    "\\textbf{W}_{ll} & \\textbf{W}_{lu}\\\\\n",
    "\\textbf{W}_{ul} & \\textbf{W}_{uu}\n",
    "\\end{bmatrix})\\begin{bmatrix}\n",
    "\\textbf{f}_l \\\\\n",
    "\\textbf{f}_{u}\n",
    "\\end{bmatrix}\\\\\n",
    "E(f) = \\textbf{f}_{l}^{T}(\\textbf{D}_{ll}-\\textbf{W}_{ll})\\textbf{f}_{l}+\\textbf{f}_{u}^{T}(\\textbf{D}_{uu}-\\textbf{W}_{uu})\\textbf{f}_{u}-2\\textbf{f}_{u}^{T}\\textbf{W}_{ul}\\textbf{f}_{l}\n",
    "\\end{equation}\n",
    "\n",
    "能量函数$E(f)$对$\\textbf{f}_u$求偏导，并令偏导数等于0，可得\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial{E(f)}}{\\partial{\\textbf{f}_u}}=-2\\textbf{W}_{ul}\\textbf{f}_{l}+2\\textbf{f}_{u}^{T}(\\textbf{D}_{uu}-\\textbf{W}_{uu})=0 \\Rightarrow \\textbf{f}_{u}=(\\textbf{D}_{uu}-\\textbf{W}_{uu})^{-1}\\textbf{W}_{ul}\\textbf{f}_{l}\n",
    "\\end{equation}\n",
    "\n",
    "由此，可以根据标记信息$\\textbf{f}_l=[y_1,y_2,…,y_l]$以及亲和矩阵$\\textbf{W}$得出未标记样本的预测标签$\\textbf{f}_{u}$。\n",
    "\n",
    "上述过程可以表示为一个二分类的标记传播方法，通过将有标记样本的标记信息在无标记样本中进行传播，可以得到未标记样本的预测标签。对于多分类问题，我们定义一个非负标记矩阵$\\textbf{F}$，将矩阵$\\textbf{F}$按照如下方式进行初始化\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{F}_{ij}^{(0)}=\\begin{cases}\n",
    "1, & if \\ 1 \\le i \\le l \\ and \\ y_i=j\\\\\n",
    "0, & ohterwise\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "基于亲和矩阵$\\textbf{W}$构造一个标记传播矩阵$\\textbf{S}$\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{S}=\\textbf{D}^{-\\frac{1}{2}}\\textbf{W}\\textbf{D}^{-\\frac{1}{2}}\\\\\n",
    "\\textbf{D}^{-\\frac{1}{2}}=\\begin{bmatrix}\n",
    "\\frac{1}{\\sqrt{d_1}} & 0 & 0 & \\cdots & 0\\\\\n",
    "0 & \\frac{1}{\\sqrt{d_2}} & 0 & \\cdots & 0\\\\\n",
    "0 & 0 & \\cdots & \\cdots & 0 & \\\\\n",
    "0 & 0 & 0 & 0 & \\frac{1}{\\sqrt{d_m}}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "在迭代过程中，通过下式更新矩阵$\\textbf{F}$\n",
    "\n",
    "\\begin{equation}\n",
    "\\textbf{F}^{(t+1)} = \\alpha\\textbf{S}\\textbf{F}^{t}+(1-\\alpha)\\textbf{F}^{(0)}\n",
    "\\end{equation}\n",
    "\n",
    "迭代结束后，根据下式确定为标记样本的类别标记\n",
    "\n",
    "\\begin{equation}\n",
    "y_i = \\underset{j\\in Y}\\max \\textbf{F}_{ij}, l+1 \\le i \\le m\n",
    "\\end{equation}\n",
    "\n",
    "其中$Y$是所有可能的类别标记的集合。\n",
    "\n",
    "$\\textbf{标签传播算法的流程如下所示:}$\n",
    "\n",
    "<img src=picture/SemiSup1.png>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{9.3 标签传播算法的实现}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import numpy as np\n",
    " \n",
    "# return k neighbors index\n",
    "def navie_knn(dataSet, query, k):\n",
    "    numSamples = dataSet.shape[0]\n",
    " \n",
    "    ## step 1: calculate Euclidean distance\n",
    "    diff = np.tile(query, (numSamples, 1)) - dataSet\n",
    "    squaredDiff = diff ** 2\n",
    "    squaredDist = np.sum(squaredDiff, axis = 1) # sum is performed by row\n",
    " \n",
    "    ## step 2: sort the distance\n",
    "    sortedDistIndices = np.argsort(squaredDist)\n",
    "    if k > len(sortedDistIndices):\n",
    "        k = len(sortedDistIndices)\n",
    " \n",
    "    return sortedDistIndices[0:k]\n",
    " \n",
    " \n",
    "# build a big graph (normalized weight matrix)\n",
    "def buildGraph(MatX, kernel_type, rbf_sigma = None, knn_num_neighbors = None):\n",
    "    num_samples = MatX.shape[0]\n",
    "    affinity_matrix = np.zeros((num_samples, num_samples), np.float32)\n",
    "    if kernel_type == 'rbf':\n",
    "        if rbf_sigma == None:\n",
    "            raise ValueError('You should input a sigma of rbf kernel!')\n",
    "        for i in range(num_samples):\n",
    "            row_sum = 0.0\n",
    "            for j in range(num_samples):\n",
    "                diff = MatX[i, :] - MatX[j, :]\n",
    "                affinity_matrix[i][j] = np.exp(sum(diff**2) / (-2.0 * rbf_sigma**2))\n",
    "                row_sum += affinity_matrix[i][j]\n",
    "            affinity_matrix[i][:] /= row_sum\n",
    "    elif kernel_type == 'knn':\n",
    "        if knn_num_neighbors == None:\n",
    "            raise ValueError('You should input a k of knn kernel!')\n",
    "        for i in range(num_samples):\n",
    "            k_neighbors = navie_knn(MatX, MatX[i, :], knn_num_neighbors)\n",
    "            affinity_matrix[i][k_neighbors] = 1.0 / knn_num_neighbors\n",
    "    else:\n",
    "        raise NameError('Not support kernel type! You can use knn or rbf!')\n",
    "    \n",
    "    return affinity_matrix\n",
    " \n",
    " \n",
    "# label propagation\n",
    "def labelPropagation(Mat_Label, Mat_Unlabel, labels, kernel_type = 'rbf', rbf_sigma = 1.5, \\\n",
    "                    knn_num_neighbors = 10, max_iter = 500, tol = 1e-3):\n",
    "    # initialize\n",
    "    num_label_samples = Mat_Label.shape[0]\n",
    "    num_unlabel_samples = Mat_Unlabel.shape[0]\n",
    "    num_samples = num_label_samples + num_unlabel_samples\n",
    "    labels_list = np.unique(labels)\n",
    "    num_classes = len(labels_list)\n",
    "    \n",
    "    MatX = np.vstack((Mat_Label, Mat_Unlabel))\n",
    "    clamp_data_label = np.zeros((num_label_samples, num_classes), np.float32)\n",
    "    for i in range(num_label_samples):\n",
    "        clamp_data_label[i][labels[i]] = 1.0\n",
    "    \n",
    "    label_function = np.zeros((num_samples, num_classes), np.float32)\n",
    "    label_function[0 : num_label_samples] = clamp_data_label\n",
    "    label_function[num_label_samples : num_samples] = -1\n",
    "    \n",
    "    # graph construction\n",
    "    affinity_matrix = buildGraph(MatX, kernel_type, rbf_sigma, knn_num_neighbors)\n",
    "    \n",
    "    # start to propagation\n",
    "    iter = 0; pre_label_function = np.zeros((num_samples, num_classes), np.float32)\n",
    "    changed = np.abs(pre_label_function - label_function).sum()\n",
    "    while iter < max_iter and changed > tol:\n",
    "        #if iter % 1 == 0:\n",
    "            #print (\"---> Iteration %d/%d, changed: %f\" % (iter, max_iter, changed))\n",
    "        pre_label_function = label_function\n",
    "        iter += 1\n",
    "        \n",
    "        # propagation\n",
    "        label_function = np.dot(affinity_matrix, label_function)\n",
    "        \n",
    "        # clamp\n",
    "        label_function[0 : num_label_samples] = clamp_data_label\n",
    "        \n",
    "        # check converge\n",
    "        changed = np.abs(pre_label_function - label_function).sum()\n",
    "    \n",
    "    # get terminate label of unlabeled data\n",
    "    unlabel_data_labels = np.zeros(num_unlabel_samples)\n",
    "    for i in range(num_unlabel_samples):\n",
    "        unlabel_data_labels[i] = np.argmax(label_function[i+num_label_samples])\n",
    "    \n",
    "    return unlabel_data_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为展示标签传播算法的运行过程，在随机生成的数据集上采用上述实现的标签传播算法进行无监督学习，代码预实验结果如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "import math\n",
    "import numpy as np\n",
    "# from LabelPropagation import labelPropagation\n",
    " \n",
    "# show\n",
    "def show(Mat_Label, labels, Mat_Unlabel, unlabel_data_labels): \n",
    "    import matplotlib.pyplot as plt \n",
    "    \n",
    "    for i in range(Mat_Label.shape[0]):\n",
    "        if int(labels[i]) == 0:  \n",
    "            plt.plot(Mat_Label[i, 0], Mat_Label[i, 1], 'Dr')  \n",
    "        elif int(labels[i]) == 1:  \n",
    "            plt.plot(Mat_Label[i, 0], Mat_Label[i, 1], 'Db')\n",
    "        else:\n",
    "            plt.plot(Mat_Label[i, 0], Mat_Label[i, 1], 'Dy')\n",
    "    \n",
    "    for i in range(Mat_Unlabel.shape[0]):\n",
    "        if int(unlabel_data_labels[i]) == 0:  \n",
    "            plt.plot(Mat_Unlabel[i, 0], Mat_Unlabel[i, 1], 'or')  \n",
    "        elif int(unlabel_data_labels[i]) == 1:  \n",
    "            plt.plot(Mat_Unlabel[i, 0], Mat_Unlabel[i, 1], 'ob')\n",
    "        else:\n",
    "            plt.plot(Mat_Unlabel[i, 0], Mat_Unlabel[i, 1], 'oy')\n",
    "    \n",
    "    plt.xlabel('X1'); plt.ylabel('X2') \n",
    "    plt.xlim(0.0, 12.)\n",
    "    plt.ylim(0.0, 12.)\n",
    "    plt.show()  \n",
    " \n",
    " \n",
    "def loadCircleData(num_data):\n",
    "    center = np.array([5.0, 5.0])\n",
    "    radiu_inner = 2\n",
    "    radiu_outer = 4\n",
    "    num_inner = int(num_data / 3)\n",
    "    num_outer = num_data - num_inner\n",
    "    \n",
    "    data = []\n",
    "    theta = 0.0\n",
    "    for i in range(num_inner):\n",
    "        pho = (theta % 360) * math.pi / 180\n",
    "        tmp = np.zeros(2, np.float32)\n",
    "        tmp[0] = radiu_inner * math.cos(pho) + np.random.rand(1) + center[0]\n",
    "        tmp[1] = radiu_inner * math.sin(pho) + np.random.rand(1) + center[1]\n",
    "        data.append(tmp)\n",
    "        theta += 2\n",
    "    \n",
    "    theta = 0.0\n",
    "    for i in range(num_outer):\n",
    "        pho = (theta % 360) * math.pi / 180\n",
    "        tmp = np.zeros(2, np.float32)\n",
    "        tmp[0] = radiu_outer * math.cos(pho) + np.random.rand(1) + center[0]\n",
    "        tmp[1] = radiu_outer * math.sin(pho) + np.random.rand(1) + center[1]\n",
    "        data.append(tmp)\n",
    "        theta += 1\n",
    "    \n",
    "    Mat_Label = np.zeros((2, 2), np.float32)\n",
    "    Mat_Label[0] = center + np.array([-radiu_inner + 0.5, 0])\n",
    "    Mat_Label[1] = center + np.array([-radiu_outer + 0.5, 0])\n",
    "    labels = [0, 1]\n",
    "    Mat_Unlabel = np.vstack(data)\n",
    "    return Mat_Label, labels, Mat_Unlabel\n",
    " \n",
    "def loadBandData(num_unlabel_samples):\n",
    "    #Mat_Label = np.array([[5.0, 2.], [5.0, 8.0]])\n",
    "    #labels = [0, 1]\n",
    "    #Mat_Unlabel = np.array([[5.1, 2.], [5.0, 8.1]])\n",
    "    \n",
    "    Mat_Label = np.array([[5.0, 2.], [5.0, 8.0]])\n",
    "    labels = [0, 1]\n",
    "    num_dim = Mat_Label.shape[1]\n",
    "    Mat_Unlabel = np.zeros((num_unlabel_samples, num_dim), np.float32)\n",
    "    Mat_Unlabel[:num_unlabel_samples/2, :] = (np.random.rand(num_unlabel_samples/2, num_dim) - 0.5) * np.array([3, 1]) + Mat_Label[0]\n",
    "    Mat_Unlabel[num_unlabel_samples/2 : num_unlabel_samples, :] = (np.random.rand(num_unlabel_samples/2, num_dim) - 0.5) * np.array([3, 1]) + Mat_Label[1]\n",
    "    return Mat_Label, labels, Mat_Unlabel\n",
    " \n",
    "#main function\n",
    "if __name__ == \"__main__\":\n",
    "    num_unlabel_samples = 800\n",
    "    #Mat_Label, labels, Mat_Unlabel = loadBandData(num_unlabel_samples)\n",
    "    Mat_Label, labels, Mat_Unlabel = loadCircleData(num_unlabel_samples)\n",
    "    \n",
    "    ## Notice: when use 'rbf' as our kernel, the choice of hyper parameter 'sigma' is very import! It should be\n",
    "    ## chose according to your dataset, specific the distance of two data points. I think it should ensure that\n",
    "    ## each point has about 10 knn or w_i,j is large enough. It also influence the speed of converge. So, may be\n",
    "    ## 'knn' kernel is better!\n",
    "    #unlabel_data_labels = labelPropagation(Mat_Label, Mat_Unlabel, labels, kernel_type = 'rbf', rbf_sigma = 0.2)\n",
    "    #unlabel_data_labels = labelPropagation(Mat_Label, Mat_Unlabel, labels, kernel_type = 'knn', knn_num_neighbors = 10, max_iter = 400)\n",
    "    #show(Mat_Label, labels, Mat_Unlabel, unlabel_data_labels)\n",
    "    iters = [10,50,100,150,200,250,300,350,400]\n",
    "    for epoch in iters:\n",
    "        unlabel_data_labels = labelPropagation(Mat_Label, Mat_Unlabel, labels, kernel_type = 'knn', knn_num_neighbors = 10, max_iter = epoch)\n",
    "        show(Mat_Label, labels, Mat_Unlabel, unlabel_data_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{9.4 协同训练算法}$\n",
    "\n",
    "协同训练算法是一种基于多视角学习的机器学习方法，它通过对同一输出目标的不同视角数据的学习，达到相互学习、共同进步的目的。协同训练算法解决半监督学习问题的思想是：首先在每个视图上基于有标记的样本分别训练一个学习器，然后再让每个学习器在未标记样本中去挑选自己最有把握的未标记样本，并给这些最有把握的未标记样本赋予伪标签，然后将伪标记样本提供给其他学习器作为新增的有标记样本用于更新训练。这个过程不断重复，直到两个学习器都不发生变化，或者达到预定的迭代次数为止。以下通过具有两个独立视图的学习问题来描述协同训练算法的过程。\n",
    "\n",
    "$\\textbf{协同训练算法的流程如下所示：}$\n",
    "\n",
    "$\\textbf{输入：}$\n",
    "\n",
    "有标记样本集合$D_l=\\{(<\\textbf{x}_{1}^{1},\\textbf{x}_{1}^{2}>,y_1),\\cdots,(<\\textbf{x}_{l}^{1},\\textbf{x}_{l}^{2}>,y_l)\\}$, 其中$(<\\textbf{x}_{i}^{1},\\textbf{x}_{i}^{2}>,y_1）$的$<\\textbf{x}_{i}^{1},\\textbf{x}_{i}^{2}>$表示样本在不同特征视图下的特征表示，$y_i$表示样本的类别标记。 \n",
    "\n",
    "无标记样本集合$D_u=\\{(<\\textbf{x}_{1}^{1},\\textbf{x}_{1}^{2}>),\\cdots,(<\\textbf{x}_{l}^{1},\\textbf{x}_{l}^{2}>)\\}$ \n",
    "\n",
    "缓冲池大小：$s$\n",
    "\n",
    "每次迭代挑选的正例和反例数：$p, n$\n",
    "\n",
    "基本学习算法：$h$\n",
    "\n",
    "最大迭代次数： $T$\n",
    "\n",
    "$\\textbf{输出：}$\n",
    "\n",
    "在两个视图上的分类器$h_1$和$h_2$\n",
    "\n",
    "$\\textbf{过程：}$\n",
    "\n",
    "(1)从$D_u$中随机抽取$s$个样本构成缓冲池$D_s$.\n",
    "\n",
    "(2)$D_u=D_u-D_s$.\n",
    "\n",
    "(3)for $j=1:2$ do:\n",
    "\n",
    "(4)$D_{i}^{j}=\\{(\\textbf{x}_{i}^{j},y_i)| (<\\textbf{x}_{i}^{1},\\textbf{x}_{i}^{2}>,y_i) \\in D_l\\}$ #获取不同视图下的有标记训练样本\n",
    "\n",
    "(5)end for\n",
    "\n",
    "(6)for $t=1:T$ do\n",
    "\n",
    "(7)for j=1:2 do\n",
    "\n",
    "(8)在数据集$D_{l}^{j}$上学习得到模型$h_j$\n",
    "\n",
    "(9)计算模型$h_j$在缓冲池样本$D_{s}^{j}$上的分类置信度,并挑选$p$个正例置信度最高的样本和$n$个负例置信度最高的样本，生成伪标签，构成伪标签样本集合$D_{p}^{j},D_{n}^{j}$.\n",
    "\n",
    "(10)$D_s=D_s-(D_p^{j} \\cup D_n^{j})$\n",
    "\n",
    "(11) end for\n",
    "\n",
    "(12) 如果当前迭代次数，在两个视图上学习得到的模型$h_1,h_2$都没有变化，结束迭代，否则\n",
    "\n",
    "(13) for j=1:2 do\n",
    "\n",
    "(14)$D_{l}^{j}=D_{l}^{j}\\cup(D_p^j \\cup D_n^j)$ #将伪标签样本放入训练样本中\n",
    "\n",
    "(15)end for\n",
    "\n",
    "(16)从未标记数据集$D_u$中随机抽取$2p+2n$个样本加入缓冲池$D_s$中.\n",
    "\n",
    "(17)end for .    直到#$T$次迭代结束\n",
    "\n",
    "(18) return $h_1,h_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{9.5 协同训练算法的实现}$\n",
    "\n",
    "(1) 以下展示在两个不同的视图上，采用协同训练算法，对同一个目标进行学习，代码如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import copy\n",
    "class CoTrainingClassifier(object):\n",
    "    \"\"\"\n",
    "    参数:\n",
    "    clf - 视图一上的分类器\n",
    "        (如果没有指定clf2,则视图二上使用与视图一相同的分类器).\n",
    "    clf2 - (可选) 视图二上的分类器\n",
    "    p - (可选) 每次迭代过程中被标记的正类样本个数\n",
    "    n - (可选) 每次迭代过程中被标记的负类样本个数\n",
    "    k - (可选) 最大迭代次数\n",
    "    u - (可选) 缓冲池的大小\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, clf, clf2=None, p=-1, n=-1, k=30, u = 75):\n",
    "        self.clf1_ = clf\t\t\n",
    "        #如果没有特别设置，视图二的分类器与视图一相同\n",
    "        if clf2 == None:\n",
    "            self.clf2_ = copy.copy(clf)\n",
    "        else:\n",
    "            self.clf2_ = clf2\n",
    "        #if they only specify one of n or p, through an exception\n",
    "        if (p == -1 and n != -1) or (p != -1 and n == -1):\n",
    "            raise ValueError('n和p，不能只设置一个，要么都设置，要么都不设置')\n",
    "        self.p_ = p\n",
    "        self.n_ = n\n",
    "        self.k_ = k\n",
    "        self.u_ = u\n",
    "        random.seed()\n",
    "\n",
    "    def fit(self, X1, X2, y):\n",
    "        \"\"\"\n",
    "        参数:\n",
    "        X1 - 数组 (n_samples, n_features_1): 视图一上的特征\n",
    "        X2 - 数组 (n_samples, n_features_2): 视图二上的特征\n",
    "        y - 数组 (n_samples): 样本的标签，-1表示未标记\n",
    "        \"\"\"\t\n",
    "        y = np.asarray(y)\n",
    "        #如果没有设置n,p，则根据数据集自动设置\n",
    "        if self.p_ == -1 and self.n_ == -1:\n",
    "            num_pos = sum(1 for y_i in y if y_i == 1)\n",
    "            num_neg = sum(1 for y_i in y if y_i == 0)\t\t\t\n",
    "            n_p_ratio = num_neg / float(num_pos)\t\t\n",
    "            if n_p_ratio > 1:\n",
    "                self.p_ = 1\n",
    "                self.n_ = round(self.p_*n_p_ratio)\n",
    "            else:\n",
    "                self.n_ = 1\n",
    "                self.p_ = round(self.n_/n_p_ratio)\n",
    "        assert(self.p_ > 0 and self.n_ > 0 and self.k_ > 0 and self.u_ > 0)\n",
    "\n",
    "        #未标记数据样本\n",
    "        U = [i for i, y_i in enumerate(y) if y_i == -1]\t\t\n",
    "        random.shuffle(U)\n",
    "        #放入缓冲池中的样本\n",
    "        U_ = U[-min(len(U), self.u_):]\n",
    "        #已标记的数据样本\n",
    "        L = [i for i, y_i in enumerate(y) if y_i != -1]\n",
    "        #将缓冲池中的样本从未标记样本中删除\n",
    "        U = U[:-len(U_)]\n",
    "        it = 0\n",
    "        #迭代训练，直到满足结束条件\n",
    "        while it != self.k_ and U:\n",
    "            it += 1\n",
    "        #在两个视图上分别训练分类器\n",
    "            self.clf1_.fit(X1[L], y[L])\n",
    "            self.clf2_.fit(X2[L], y[L])\n",
    "        #在两个视图上分别预测缓冲池值的未标记样本\n",
    "            y1_prob = self.clf1_.predict_proba(X1[U_])\n",
    "            y2_prob = self.clf2_.predict_proba(X2[U_])\n",
    "\n",
    "            n, p = [], []\n",
    "\n",
    "            for i in (y1_prob[:,0].argsort())[-self.n_:]:\n",
    "                if y1_prob[i,0] > 0.5:\n",
    "                    n.append(i)\n",
    "            for i in (y1_prob[:,1].argsort())[-self.p_:]:\n",
    "                if y1_prob[i,1] > 0.5:\n",
    "                    p.append(i)\n",
    "\n",
    "            for i in (y2_prob[:,0].argsort())[-self.n_:]:\n",
    "                if y2_prob[i,0] > 0.5:\n",
    "                    n.append(i)\n",
    "            for i in (y2_prob[:,1].argsort())[-self.p_:]:\n",
    "                if y2_prob[i,1] > 0.5:\n",
    "                    p.append(i)\n",
    "            #为缓冲池值的未标记样本赋予伪标签\n",
    "            y[[U_[x] for x in p]] = 1\n",
    "            y[[U_[x] for x in n]] = 0\n",
    "        #将伪标签样本加入到已标记样本集合中，用于下一次训练\n",
    "            L.extend([U_[x] for x in p])\n",
    "            L.extend([U_[x] for x in n])\n",
    "        #从缓冲池值删除伪标记样本，并加入新的未标记样本\n",
    "            U_ = [elem for elem in U_ if not (elem in p or elem in n)]\t\t\t\n",
    "            add_counter = 0 \n",
    "            num_to_add = len(p) + len(n)\n",
    "            while add_counter != num_to_add and U:\n",
    "                add_counter += 1\n",
    "                U_.append(U.pop())\n",
    "        #最终的分类器训练\n",
    "        self.clf1_.fit(X1[L], y[L])\n",
    "        self.clf2_.fit(X2[L], y[L])\n",
    "    #检查分类器是否支持概率预测\n",
    "    def supports_proba(self, clf, x):\t\t\n",
    "        try:\n",
    "            clf.predict_proba([x])\n",
    "            return True\n",
    "        except:\n",
    "            return False\n",
    "    #协同训练算法的预测函数\n",
    "    def predict(self, X1, X2):\n",
    "        \"\"\"\n",
    "        参数:\n",
    "        X1 - 数组 (n_samples, n_features1)：视图一的特征\n",
    "        X2 - 数组 (n_samples, n_features2)：视图二的特征\t\t\n",
    "        输出:\n",
    "        y - 数组 (n_samples)： 预测类别输出\t\t\n",
    "        \"\"\"\n",
    "        y1 = self.clf1_.predict(X1)\n",
    "        y2 = self.clf2_.predict(X2)\n",
    "        proba_supported = self.supports_proba(self.clf1_, X1[0]) and self.supports_proba(self.clf2_, X2[0])\t\t\n",
    "        y_pred = np.asarray([-1] * X1.shape[0])\n",
    "        for i, (y1_i, y2_i) in enumerate(zip(y1, y2)):\n",
    "            if y1_i == y2_i:\n",
    "                y_pred[i] = y1_i\n",
    "            elif proba_supported:\n",
    "                y1_probs = self.clf1_.predict_proba([X1[i]])[0]\n",
    "                y2_probs = self.clf2_.predict_proba([X2[i]])[0]\n",
    "                sum_y_probs = [prob1 + prob2 for (prob1, prob2) in zip(y1_probs, y2_probs)]\n",
    "                max_sum_prob = max(sum_y_probs)\n",
    "                y_pred[i] = sum_y_probs.index(max_sum_prob)\n",
    "            else:\n",
    "                #如果两个分类器的结果不一致，且不支持概率预测，则随机猜测\n",
    "                y_pred[i] = random.randint(0, 1)\t\t\n",
    "        assert not (-1 in y_pred)\n",
    "        return y_pred\n",
    "    #协同训练算法的概率预测\n",
    "    def predict_proba(self, X1, X2):\t\t\n",
    "        y_proba = np.full((X1.shape[0], 2), -1)\n",
    "        y1_proba = self.clf1_.predict_proba(X1)\n",
    "        y2_proba = self.clf2_.predict_proba(X2)\n",
    "        for i, (y1_i_dist, y2_i_dist) in enumerate(zip(y1_proba, y2_proba)):\n",
    "            y_proba[i][0] = (y1_i_dist[0] + y2_i_dist[0]) / 2\n",
    "            y_proba[i][1] = (y1_i_dist[1] + y2_i_dist[1]) / 2\n",
    "        _epsilon = 0.0001\n",
    "        assert all(abs(sum(y_dist) - 1) <= _epsilon for y_dist in y_proba)\n",
    "        return y_proba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) 为展示协同训练算法的性能，生成一个分类数据集，采用数据中前一半的特征属性作为一个视图，剩下的一半特征属性作为第二个视图，两个视图对应同一个输出目标变量，以随机森林作为学习器，采用协同训练算法，展示在原始数据上进行单一的随机森林学习与在两个视图上进行协同训练得到的分类模型的新能差异。实现代码和实验结果如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RandomForestClassifier\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.83      0.88      0.86      3136\n",
      "           1       0.87      0.82      0.85      3114\n",
      "\n",
      "    accuracy                           0.85      6250\n",
      "   macro avg       0.85      0.85      0.85      6250\n",
      "weighted avg       0.85      0.85      0.85      6250\n",
      "\n",
      "RandomForestClassifier CoTraining\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.82      0.88      0.85      3136\n",
      "           1       0.87      0.81      0.84      3114\n",
      "\n",
      "    accuracy                           0.85      6250\n",
      "   macro avg       0.85      0.85      0.85      6250\n",
      "weighted avg       0.85      0.85      0.85      6250\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.datasets import make_classification\n",
    "N_SAMPLES = 25000\n",
    "N_FEATURES = 1000\n",
    "X, y = make_classification(n_samples=N_SAMPLES, n_features=N_FEATURES)\n",
    "\n",
    "y[:N_SAMPLES//2] = -1\n",
    "\n",
    "X_test = X[-N_SAMPLES//4:]\n",
    "y_test = y[-N_SAMPLES//4:]\n",
    "\n",
    "X_labeled = X[N_SAMPLES//2:-N_SAMPLES//4]\n",
    "y_labeled = y[N_SAMPLES//2:-N_SAMPLES//4]\n",
    "\n",
    "y = y[:-N_SAMPLES//4]\n",
    "X = X[:-N_SAMPLES//4]\n",
    "\n",
    "\n",
    "X1 = X[:,:N_FEATURES // 2]\n",
    "X2 = X[:, N_FEATURES // 2:]\n",
    "\n",
    "\n",
    "print ('RandomForestClassifier')\n",
    "base_lr = RandomForestClassifier()\n",
    "base_lr.fit(X_labeled, y_labeled)\n",
    "y_pred = base_lr.predict(X_test)\n",
    "print (classification_report(y_test, y_pred))\n",
    "\n",
    "print ('RandomForestClassifier CoTraining')\n",
    "lg_co_clf = CoTrainingClassifier(RandomForestClassifier())\n",
    "lg_co_clf.fit(X1, X2, y)\n",
    "y_pred = lg_co_clf.predict(X_test[:, :N_FEATURES // 2], X_test[:, N_FEATURES // 2:])\n",
    "print (classification_report(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{9.6 实践任务}$\n",
    "\n",
    "在弱监督信息条件下进行学习已成为机器学习领域的热点研究课题。偏标记学习是一类重要的弱监督学习框架，在该框架下每个输入对象在输入空间有单个特征向量进行刻画，而在输出空间与一组候选标记相关联，其中仅有一个为其真实标记。请参考本章实现的标签传播算法，以及以下论文，构建一个偏标记学习系统。\n",
    "论文[1]: 张敏灵. 偏标记学习研究综述[J]. 数据采集预处理, 30(1): 77-87, 2015.\n",
    "论文[2]:  Zhang M , F Yu. Solving the partial label learning problem: an instance-based approach. AAAI, 2015."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#添加代码，完成实践任务"
   ]
  }
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